Microscopic Derivation of Ginzburg-Landau Theory
Rupert L. Frank, Christian Hainzl, Robert Seiringer, Jan Philip, Solovej
TL;DR
This paper rigorously derives the Ginzburg-Landau theory from the microscopic BCS model near the critical temperature, using semiclassical analysis with minimal assumptions.
Contribution
It provides the first rigorous mathematical derivation of Ginzburg-Landau theory starting from the microscopic BCS model.
Findings
Ginzburg-Landau theory emerges as an effective macroscopic theory near critical temperature.
The derivation uses semiclassical analysis with minimal regularity assumptions.
The work bridges microscopic BCS theory and macroscopic Ginzburg-Landau description.
Abstract
We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof.
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